In this study, we consider free boundary problems for nonlinear advection–diffusion equations of the form ut−uxx+βux=f(u) for t>0, g(t)<x<h(t), where x=g(t) and x=h(t) are free boundaries. This problem may be used to describe the spreading of a biological or chemical species where the free boundaries represent the expanding fronts. When f is a logistic nonlinearity, it has been shown that the asymptotic spreading speeds of the two fronts h(t) and g(t) are different due to the advection term. In this study, for monostable, bistable, and combustion types nonlinearities, we give much sharper estimates of the different spreading speeds of the fronts, and we also prove that the solution converges to a semi-wave in C2-norm as t→∞ when spreading occurs. We develop new approaches and extend a previous result to the problem with the advection term.